hello everyone:smile:
for
i=1,2,...,(n+1)
let P_{i}(X)=\frac{\prod_{1\leq j\leq n+1,j\neq i}(X-a_j)}{\prod_{1\leq j\leq n+1,j\neq i}(a_i-a_j)}
prove that
(P_1,P_2,...P_{n+1})
is basis of
\mathbb{R}_{n}[X]
.
i already have an answer but i don't understand some of it.
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we have...